Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
The given function is
f(x) = x³ - 9x² + 26x - 24
It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).
According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.
Use synthetic method to divide f(x) by (x-2).
f(x) = (x - 2) (x² - 7x + 12)
f(x)= (x - 2) (x² - 4x - 3x + 12)
f(x)= (x - 2) (x(x - 4) - 3(x - 4))
f(x)= (x - 2) (x - 4) (x - 3)
To find the roots equation the function equate the function equal to 0.
0 = (x - 2) (x - 4) (x - 3)
Equate each factor equal to 0.
x = 2,3,4
Therefore the roots of the function are 2,3 and 4.
(btw this is someone else's answer i found since i got a little confused myself heh)
Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
\The roots of the of the function are 2,3 and 4.
What is the measure of angle x?
A) 65
B) 25
C) 115
D) 125
Answer: 65°
Step-by-step explanation: We are assuming that these lines are ║.
If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
Since x and 65 lie on alternate side of the transversal and
on the interior of the two lines, we know that x = 65.
It costs $7.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost decreases to $5.75 per hour.
How much would it cost to rent a kayak for 6 hours?
Answer:
7.15 times 5 plus 5.75=$41.5
Step-by-step explanation:
Answer:
$41.50
Step-by-step explanation:
Multiply 7.15 by 5. This represents how much it costs for the first 5 hours.Add 5.75 to the product. This is the extra hour with the reduced price.Anyone understand how to do this??
Answer:
T=-11
Step-by-step explanation:
y2-y1/x2-x1
=t-(-1)/9-10
=t+1/9-10
=t+1/-1
=-11+1/1
=-10/1
=-10
Hope this helps :)
2.5(a + 4) + 0.5a = 12.4
Answer:
a=0.8
Step-by-step explanation:
First I distributed 2.5 into (a+4) and got (2.5a+10)+0.5a=12.4. I then combined like terms which are 2.5a and 0.5a and got 3a+10=12.4. I subtracted 10 from both sides to get rid of it and got 3a=2.4. Later, I divided 3 from both sides to get a which comes out to be 0.8.
Hope this helps you :)
RT and UW are parallel lines. Which angles are vertical angles? HELP ASAAPPP
<uvx and <tsv
<uvx and <WVS
<uvx and <tsq
<uvx and <rsq
Answer:
It is <uvx and <WVS..........
Answer:
<uvx and <wvs
Step-by-step explanation:
Other vertical angles include:
<xvw and <uvs
<vst and <rsq
<rsv and <qst
Vertical angles are angles that are on opposite sides of eachother and are equal to eachother.
Sandra eats about 2000 calories per day with LaTeX: \frac{1}{4}1 4 of her calories from fat and LaTeX: \frac{1}{5}1 5 from carbohydrates. How many total calories does Sandra get from both fat and carbohydratesSandra eats about 2000 calories per day with LaTeX: \frac{1}{4}1 4 of her calories from fat and LaTeX: \frac{1}{5}1 5 from carbohydrates. How many total calories does Sandra get from both fat and carbohydrates
Answer:
Calories from both fat and carbohydrates = 900 calories/day
Step-by-step explanation:
Number of calories eaten by Sandra per day = 2000 calories/day
Calories from fat = [tex]\frac{1}{4}[/tex] of the total number of calories per day
OR
Calories from fat = [tex]\frac{1}{4}\times 2000 = 500\ calories/day[/tex]
Calories from carbohydrates = [tex]\frac{1}{5}[/tex] of the total number of calories per day
OR
Calories from carbohydrates = [tex]\frac{1}{5}\times 2000 = 400\ calories/day[/tex]
To find the total number of calories from both fat and carbohydrates, we need to add the calories from fat and calories from carbohydrates as calculated above.
Calories from both fat and carbohydrates = Calories from fat + Calories from carbohydrates = 500 + 400 = 900 calories/day
The shortest side of a right triangle is 14 inches long. The difference between the lengths of the other two sides is 2 inches. Find the missing sides. Use exact values.
Answer:
The missing sides are 50 inches and 48 inches long.
Step-by-step explanation:
Let the lengths of the other two sides be x inches and y inches
And let x represent the length of the longest side.
From the question,
The difference between the lengths of the other two sides is 2 inches. That is,
x - y = 2 ...... (1)
The three sides of the right triangle are x, y, and 14 inches long.
From the Pythagorean theorem, " In a right triangle, the square of the longest side equals sum of squares of the other two sides"
Here, the longest side is x
Hence, we can write that
x² = y² + 14²
∴ x² = y² + 196 ...... (2)
Now, we have two equations, we can then solve simultaneously.
From equation (1)
x - y = 2
∴ x = y + 2 ...... (3)
Put this into equation (2)
x² = y² + 196
(y+2)² = y² + 196
y² + 4y + 4 = y² + 196
4y + 4 = 196
4y = 196 - 4
4y = 192
y = 192/4
y = 48
To determine x, we will substitute the value of y into equation (3)
x = y + 2
∴ x = 48 + 2
x = 50
Hence, x = 50 and y = 48
Since the lengths of the other two sides are x inches and y inches,
Hence, the missing sides are 50 inches and 48 inches.
A student ate 3/20 of all the candy and another 1.2 lb. Another student ate 3/5 of the candy and the remaining 0.3 lb. What was the total weight of the candy they ate?
Answer:
x = 6 lb
Step-by-step explanation:
Let
Total weight of the candy = x
3/20x + 1.2 lb + 3/5x + 0.3 lb = x
3/20x + 3/5x + 1.5 lb = x
3x+12x/20 + 1.5 lb = x
15/20x + 1.5 = x
1.5 = x - 15/20x
1.5 =20x -15x /20
1.5 = 5/20x
1.5 = 1/4x
x = 1.5 ÷ 1/4
= 1.5 × 4/1
= 6
x = 6 lb
Quiz 1
Rewrite the fraction as a decimal.
13
10
Report a pro
Answer:
1.3
Step-by-step explanation:
Just divide the top by the bottom.
Answer:
1.3
Step-by-step explanation:
If we divide 13 by 10, our answer is 1.3. This makes sense since the proper fraction would be 1 & 3/10 (one and three-tenths.) Three-tenths is equal to 30% or 0.3.
Pls help me asap!!!!
Need answer ASAP will give brainliest check out the picture
Answer:
i think... x=6
Step-by-step explanation:
3x+9=x+21
3x−x=12
2x=12
x=6
Can someone help me find the measure of each angle in the triangle?
Answer:Remember -- the sum of the degree measures of angles in any triangle equals 180 degrees. ... So, the measure of angle A + angle B + angle C = 180 degrees. ... If a triangle is equilateral, what is the degree measure of each of its angles?
Step-by-step explanation:
Answer-
the sum of the degree measures of angles in any triangle equals 180 degrees. ... So, the measure of angle A + angle B + angle C = 180 degrees. ... If a triangle is equilateral, what is the degree measure of each of its angles?
4. A student buys a movie to watch on her phone, but she's worried about the
amount of storage space downloading it will take up. She starts the download and
notices it will download at a constant rate. After 3 minutes, she checks her phone
and sees that she has 2,345 MB of space available. She checks her phone after 7
minutes and notices that she now has 2,105 MB of space available.
(a) How many MB of available storage are being filled by the movie per minute?
Answer:
240
Step-by-step explanation:
by minusing the both values it'll be 240
The rate at which the storage space of the mobile gets filled by the movie is - 60 MB per minute.
Given that,
A student buys a movie to watch on her phone
it will download at a constant rate.
After 3 minutes, she checks her phone and sees that she has 2,345 MB of space available.
She checks her phone after 7 minutes and notices that she now has 2,105 MB of space available.
The rate of change is defined as the change in value with the rest of the time is called rate of change.
Here,
Rate = (storage available after 3 minutes) - (storage available after 7 min)]
---------------------------------------------------------------------------------------------
Time interval
Rate = (2,345 - 2105 ) / (3 - 7)
Rate = - 240 / - 4
Rate = - 60
Where negative sign shows that the amount of storage getting reduced.
Thus, the rate at which the storage space of the mobile gets filled by the movie is - 60 MB per minute.
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ASAP Can somebody plz answer all of them correct except for #1 thanks!
(Only if u done this before)
WILL MARK BRAINLIEST
Answer:
For number 2 that is going to be 1 4/5
number 3 is going to be 5 4/7
Number 4 is going to be 8 1/3
Number 5 is going to be 3 1/6
Number 6 is going to be 6 3/11
Step-by-step explanation:
I hoped this helps
Yaneev thinks of a number y. He subtracts three from the number, then doubles it. What is the final result, in terms of y?
Answer:
y = 6
Step-by-step explanation:
2(y - 3) = y
2y - 6 = y
y = 6
Hope that works out :)
Adam, Bethany and Charles played a game.
Adam scored 8 more points than Charles.
Bethany scored 5 more points than Adam.
They scored a total of 72 points.
Find the number of points that Adam, Bethany and Charles each scored.
Points scored by Adam, Bethany and Charles are 25, 17 and 30 respectively.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Adam scored 8 more points than Charles,
And Bethany scored 5 more points than Adam.
Also, total score is 72.
Let points scored by Adam is x,
Then point scored by Charles = x-8,
And point scored by Bethany = x+5.
Since, total score = 72
x + x-8 + x+5 = 72
3x - 3 = 72
3x = 75
x = 25
Points scored by Adam is x = 25,
Point scored by Charles = x-8 = 17,
And point scored by Bethany = x+5 = 30.
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Travis was attempting to make muffins to take to a neighbor that had just moved in down the street. The recipe that he was using required 3/4 cup of sugar and 1/8 cup of butter.
1. Travis accidentally put a whole cup of butter in the mix.
A. What is the ratio of sugar to butter in the original recipe? What amount of sugar does Travis need to put into the mix to have the same ratio of sugar to butter that the original recipe calls for?
B. If Travis wants to keep the ratios the same as they are in the original recipe, how will the amounts of all the other ingredients for this new mixture compare to the amounts for a single batch of muffins?
C. The original recipe called for 3/8 cup of blueberries. What is the ratio of blueberries to butter in the recipe? How many cups of blueberries are needed in the new enlarged mixture?
Answer:
A. (3/4) : (1/8)
Travis must add 6 cups of sugar to maintain the ratio.
B. Travis must multiply the ratio of all other ingredients by 8.
C. (3/8) : (1/8)
Travis must add 3 cups of blueberries to maintain the ratio.
Step-by-step explanation:
A.
3/4 * 8
24/4
6 cups of sugar to maintain the same ratio.
B. 1/8 turned into 1 so that means it was multiplied by 8
C. 3/8 are blueberries and 1/8 is butter
(3/8) * 8
3
This took a long time to do... reward?
please help! asap! thanks! xoxoxo
Answer:
B
Step-by-step explanation:
Don't know how to type those here so see attachment
Answer:
x = √29
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 2^2 = c^2
25 + 4 = c^2
29 = c^2
√29 = √c^2
√29 = c
x = √29
Bob runs a total of 12 miles each week. He wants to increase the number of miles he runs each week by 1.5 miles until he is running a total of 26 miles each week. Provide an equation that can be used to determine the number of weeks Bob will need to reach his goal
Answer:
The equation is 12 + 1.5w = 26
Step-by-step explanation:
Each week running = 12 miles
He wants to increase the number of miles he runs each week by 1.5 miles until he is running a total of 26 miles each week.
12 + 1.5w = 26
Where,
w = number of weeks to reach his goal
12 + 1.5w = 26
1.5w = 26 - 12
1.5w = 14
Divide both sides by 1.5
w = 14 / 1.5
= 9.33 weeks
help me on problem 4 !!!!I WILL GIVE BRAINLIEST!!!!!
Answer:
b=12.20
Step-by-step explanation:
its asking for a triangle. there are two legs (the straight sides) and a hypotenuse*.( the slanted one) the formula for finding a missing side is a2+b2=c2. (squared) then you plug in your numbers. and c2 is always the slanted side while a and b are the legs. Sorry this was late tho.
Although you can draw an infinite number of lines through the midpoint of a
segment, you can draw only one line that is to the line segment.
Answer: Perpendicular
Step-by-step explanation: Took the quiz :)
Which of the following is equivalent to 4x-3y=15
A.4/3x-5
B.-4/3x+5
C.4/3x+15
D.3/4x-5
Answer:
the answer is A
Step-by-step explanation:
A = 4/3x-5
Answer:
Step-by-step explanation:
B
8.78 + 6.2 show you work
Answer:
14.98
Step-by-step explanation:
1
8.78
6.20
---------
14.98
Answer:
14.98
Step-by-step explanation:
8.78
+6.2
--------
14.98
you want to imagine 6.2 like 6.20
so...
8.78
+6.20
----------
14.98
the 8 goes down 7+2=9 the (.) goes down 8+6=14 14.98
hope this helps :)
What is the equation of the graphed line written in standard form?
Answer:
C. y = -2/3x -2
Step-by-step explanation:
We know the slope is negative. You can find slope using rise/run. The y-intercept is -2 because the line meets -2 at the y-intercept.
Answer:
The first answer (top)
Step-by-step explanation:
Standard form is ax+by=c
a and b are the coefficients
Take a point from the given line
I chose (0, -2)
Then, plug in the values of x and y
2*0+3*-2=-6
-6=-6
Since it works the standard form of the line is 2x+3y=-6
-16 384, 4096 -1024, 256, -64
Answer:
320
Step-by-step explanation:
i hop it work
PLEASEE HELP I WILL BRAINLISTT Question 2: Given the function defined by y = x^2, which of the following is its average rate of change from x = 2 to x = 10? *
A.5/2
B.2
C.8/3
D.12
12 is its average rate of change from x = 2 to x = 10.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Given the function defined by y = x^2
now,
its average rate of change from x = 2 to x = 10,=
=10^2-2^2/10-2
=100-4/8
96/8
=12
Hence, 12 is its average rate of change from x = 2 to x = 10.
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bicycle rental company charges a $5 flat fee plus $1.20 per hour. Select the expression that represents renting a bicycle for h hours. A. 5h + 120h B. (5 + 1.20)h C. 5 + 1.20h D. 5h + 1.20
Answer:
a
Step-by-step explanation:
Find 3/7 • 9/10 as a fraction
Answer:
27/70
Step-by-step explanation:
This is simple: First, you multiply the numerators. 3x9 is 27. That is the numerator to your answer.
Next, you multiply the denominators. 7x10 is 70. That's the denominator to the answer.
Put them together and you get 27/70.
Hope I helped!!!
Liam has a bag of b beads. He gives 20 beads to his sister. He then makes 4 necklaces with the same of beads on each necklace using all of the remaining beads. Write an expression that represents the number of beads on each necklace. Show your work.
Given :
Liam has a bag of b beads.
He gives 20 beads to his sister.
He then makes 4 necklaces with the same of beads on each necklace using all of the remaining beads.
To Find :
Write an expression that represents the number of beads on each necklace.
Solution :
Number of necklace remains after giving 20 beads to his sister is ( b - 20 ).
Number of beads on each necklace using all of the remaining beads is :
[tex]N=\dfrac{b-20}{4}[/tex]
Hence, this is the required solution.
I need help ;-; pls
Answer:
B) 17
Step-by-step explanation:
3 (12 - 8) + 5
(3 x 12) - (3 x 8) + 5
(36 - 24) + 5
12 + 5
17